Are you saying you replaced the probe and it is now working, or you replaced the whole controller?
Does the Inkbird read the correct temperature? Sounds like it wasn't reading the temperature, and kept cooling. Or maybe a relay stuck, and it kept cooling.
I don't have an Inkbird, but I like to test my controllers with a lamp. If the light bulb turns on when the controller reads above the set point, then I know it should be working.